Is Noise Conditioning Necessary? A Unified Theory of Unconditional Graph Diffusion Models

Explicit noise-level conditioning is widely regarded as essential for the effective operation of Graph Diffusion Models (GDMs). In this work, we challenge this assumption by investigating whether denoisers can implicitly infer noise levels directly from corrupted graph structures, potentially eliminating the need for explicit noise conditioning. To this end, we develop a theoretical framework centered on Bernoulli edge-flip corruptions and extend it to encompass more complex scenarios involving coupled structure-attribute noise. Extensive empirical evaluations on both synthetic and real-world graph datasets, using models such as GDSS and DiGress, provide strong support for our theoretical findings. Notably, unconditional GDMs achieve performance comparable or superior to their conditioned counterparts, while also offering reductions in parameters (4 -6%) and computation time (8 -10%). Our results suggest that the high-dimensional nature of graph data itself often encodes sufficient information for the denoising process, opening avenues for simpler, more efficient GDM architectures.